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KF is essentially a symbolic unrolling of a LU decomposition. There is a graphical algorithm which makes all the minutae trivial [1]. [1] https://arxiv.org/pdf

by akssri 10y ago

KF is essentially a symbolic unrolling of a LU decomposition. There is a graphical algorithm which makes all the minutae trivial [1]. [1] https://arxiv.org/pdf/1508.00952.pdf https://arxiv.org/pdf/1508.00952.pdf

andylei 10y ago
i can't tell if this is a joke or not
smallnamespace 10y ago
"'We have a new theorem--that mathematicians can only prove trivial theorems, because every theorem that's proved is trivial.'" - Richard Feynman https://books.google.com/books?id=7papZR4oVssC&pg=PA84&lpg=PA84&dq=mathematicians+can+prove+only+trivial+theorems&source=bl&ots=etU_eckSXZ&sig=fYFYlD1WVkktbgRvC13YwLYjTPU&hl=en&sa=X&ved=0ahUKEwj4romwucXPAhUr0YMKHYLaDm8Q6AEIRzAH#v=onepage&q=mathematicians%20can%20prove%20only%20trivial%20theorems&f=false https://books.google.com/books?id=7papZR4oVssC&pg=PA84&lpg=P...
akssri 10y ago
> "'We have a new theorem--that mathematicians can only prove trivial theorems, because every theorem that's proved is trivial.'" - Richard Feynman Sigh. KF is essentially solving a QP with equality constraints (Boyd's course is a good place for details), which can be solved exactly with a single decomposition of the KKT system - picking an ordering is all that matters for complexity. This is essentially the principle on which all of Sparse Linear algebra and Graphical models work. There is nothing special about the structure of KF, nor in LQR, nor in their non-linear generalizations. One can symbolically unroll Schur complements multiple times to make block-LU appear opaque and sophisticated, but it really is not (this of course is not to say this is done deliberately). KF can also derived from the Bayes' network model, but extending this to non-linear forms like EKF, and to things which are not first-order becomes rather troublesome (or impossible). I'd have appreciated a post asking for details rather than infantile derision.
- smallnamespace 10y ago
  I'm sorry that you can't take a joke. Personally, I found it funny that you're blessed with the requisite mathematical knowledge and perspective to be able to view the details as 'trivial minutiae'. I did spend 5 minutes perusing the paper you linked, and couldn't make heads or tails of it. For myself and all other mere mortals unfamiliar with this mathematical machinery, I can assure you that details are far from trivial. Thanks for taking your time to explain.
  - RBerenguel 10y ago
    Well, it's a mathematical paper. I skimmed it, and although it's not my field (well, I wonder what my field is now that I work as machine learning engineer, but it used to be dynamical systems in Banach spaces) it seems pretty much readable given a mathematical background in research. I can assure you, this is way more readable than many other papers. I can totally understand the "minutiae" comment there.

by akssri 10y ago

andylei 10y ago

i can't tell if this is a joke or not

smallnamespace 10y ago

"'We have a new theorem--that mathematicians can only prove trivial theorems, because every theorem that's proved is trivial.'" - Richard Feynman https://books.google.com/books?id=7papZR4oVssC&pg=PA84&lpg=PA84&dq=mathematicians+can+prove+only+trivial+theorems&source=bl&ots=etU_eckSXZ&sig=fYFYlD1WVkktbgRvC13YwLYjTPU&hl=en&sa=X&ved=0ahUKEwj4romwucXPAhUr0YMKHYLaDm8Q6AEIRzAH#v=onepage&q=mathematicians%20can%20prove%20only%20trivial%20theorems&f=false https://books.google.com/books?id=7papZR4oVssC&pg=PA84&lpg=P...

akssri 10y ago

> "'We have a new theorem--that mathematicians can only prove trivial theorems, because every theorem that's proved is trivial.'" - Richard Feynman Sigh. KF is essentially solving a QP with equality constraints (Boyd's course is a good place for details), which can be solved exactly with a single decomposition of the KKT system - picking an ordering is all that matters for complexity. This is essentially the principle on which all of Sparse Linear algebra and Graphical models work. There is nothing special about the structure of KF, nor in LQR, nor in their non-linear generalizations. One can symbolically unroll Schur complements multiple times to make block-LU appear opaque and sophisticated, but it really is not (this of course is not to say this is done deliberately). KF can also derived from the Bayes' network model, but extending this to non-linear forms like EKF, and to things which are not first-order becomes rather troublesome (or impossible). I'd have appreciated a post asking for details rather than infantile derision.

smallnamespace 10y ago
I'm sorry that you can't take a joke. Personally, I found it funny that you're blessed with the requisite mathematical knowledge and perspective to be able to view the details as 'trivial minutiae'. I did spend 5 minutes perusing the paper you linked, and couldn't make heads or tails of it. For myself and all other mere mortals unfamiliar with this mathematical machinery, I can assure you that details are far from trivial. Thanks for taking your time to explain.
- RBerenguel 10y ago
  Well, it's a mathematical paper. I skimmed it, and although it's not my field (well, I wonder what my field is now that I work as machine learning engineer, but it used to be dynamical systems in Banach spaces) it seems pretty much readable given a mathematical background in research. I can assure you, this is way more readable than many other papers. I can totally understand the "minutiae" comment there.